text:
Projected Area & AoA - Projected area of the wing is variable (as projected on to a surface that is perpendicular to the relative wind)
Does Wing Area vary with angle ot attack?
Edit: why we don't recognize that the projected area of the wing as variable (as projected on to a surface that is perpendicular to the relative wind)
Per the above link, for lift and drag equations the area is defined to the reference area by convention - it does not change. Why not have a variable projected area instead? Wouldn’t using projected area tell you the true values for lift and drag?

After I wrote my answer I clicked on the link in the question and realized it was about variation in "projected area" with changes in angle-of-attack, not with bank angle.  You might want to put that into your actual question, if that's what you want to know-- why we don't recognize that the area of the wing (as projected on to a surface that is parallel to the relative wind and also parallel with a line drawn from wingtip to wingtip?)  is not exactly constant as we change angle-of-attack.  Well, you could do that but you'd just end up with a slightly different curve of Cl versus aoa, right?

So, if you are asking why we don't recognize that the "projected area" of the wing varies as we vary the angle-of-attack, then -- doesn't this answer your question?  https://aviation.stackexchange.com/a/56462/34686

@Quiet flyer thank you for your answer. I should probably have reworded my question (rewording now), and thanks for the link I’ll check it out. For your answer below,

@Quiet flyer for your answer below, I understand you said it doesn’t apply to this question, but after reading it it seems that projected area wouldn’t effect lift and drag.

The convention of keeping area constant emerged in an age before computers. For efficiency, it was agreed to keep area constant and put all AoA-related changes into the coefficients. Now you need to know that the lift and drag equations are only approximations, valid only for small angles. Actually, the lift equation in full would be a Taylor series, the first element of which is $$L = \frac{\rho}{2}\cdot v^2 \cdot A \cdot c_{L\alpha} \cdot sin(\alpha) \cdot cos(\alpha)$$
To simplify things, it became customary to use $\alpha$ in radians instead of its sine and to use 1 for the cosine. Keeping the cosine would in effect give you the projected chord already but increases the computational effort. This simplification is fine for the usual range of angles of attack and the error incurred by this is negligible. However, at 90° angle of attack you will clearly see a difference and only the trigonometric functions will make the result of the equation look at least somewhat close to reality. In addition, you now need two different $c_{L\alpha}$s to get realistic results, one for the AoA regime of attached flow and one for separated flow.

Lift coefficient over the first 180°, taken from Hoerner's Fluid Dynamic Lift.

Why not have a variable projected area instead?

For simplicity in an age of slide rules. With computers, that simplification is no longer needed.

Wouldn’t using projected area tell you the true values for lift and drag?

Yes, but the difference only becomes significant when separation makes the linear equations invalid anyway.

The projected wing area relative to the airflow does indeed vary with AoA, but we don't use projected area relative to airflow around a wing for the lift & drag equations. The reference area is chosen independent of the direction of the flow - variation with flow direction is accounted for in the definition of lift coefficient C$_L$ and drag coefficient C$_D$, not in the wing area.
The airflow around an aeroplane is such that the wetted wing area would be most relevant, as stated in this answer.. But this area changes per wing profile shape - in order to obtain an independent variable, the wing area is chosen as a flat area in its widest local chord. There are standard methods defined, like stated in this answer

Ah TY - looking at your 2nd linked answer, based off the airflow properties/expected-behavior for the types of shapes of objects in the flow determines what reference areas is chosen. So cross-sectional area for short-bodies and then wetted area for long-slender-bodies/airplanes. Yet for long slender bodies it’s is still better to use projected area instead of wetted area - why if the wetted area is more accurate? Is the reason to not use wetted area because we want to compare to other wings C_d & C_L? And likewise for short bodies to use the cross section for comparing to other short bodies?

Yes indeed, for scaling purposes because of the properties of the dynamic pressure.

I know this is only current because of a bot, but why not, it is here anyway.
In principle, you could make up a new "alien" aerodynamics, where you do use projected area. The reason you can do this, is because the coefficient of lift and drag are non-dimensionalised parameters, like Mach number or Reynolds number. If we consider just 2D flow, so an aerofoil, then
$$c_l = \frac{L’}{0.5 \rho v^2 c}$$
Here you could choose to make c (the chord length) the projected chord length instead. This would be a shorter length than the geometric chord length and for the equation to be consistent, you would simply need to make $c_l$ larger. The factor would be by the same $\cos{\alpha}$ amount. This would then carry over into 3D lift, given the constituent aerofoils have a greater coefficient of lift, this would be offset by the smaller projected area.
So the key feature here is that the chord is used as an indicative length measure for the non-dimensionalising. You could just have easily used the quarter chord dimension (c/4), but then all coefficients of lift would just be 4 times larger. Obviously, using the geometric c makes things easier, because the "projected effect" is hidden in the current values we used for $c_l$. That is, the system we have now makes things easier, such that we don't need to have a $c \cos{\alpha}$ or an $S \cos{\alpha}$ (for surface area), whenever we use them.

Wouldn’t using projected area tell you the true values for lift and
drag?

No.  For a given airspeed and angle-of-attack, a wing makes the same amount of lift, and drag, regardless of the bank angle.  The "projected area" is irrelevant.
Otherwise, all you'd have to do is give a wing lots of dihedral, and it would automatically tend to roll toward wings-level whenever it was banked, regardless of whether there was any sideslip or not.  Because the lower wing would have more "projected area" than the higher wing.
That's not how it works.  The stabilizing effect of dihedral is intimately connected with sideslip, which increases the angle-of-attack of the low ("upwind") wing and decreases the angle-of-attack of the high ("downwind") wing.  Take away the sideslip, and the stabilizing effect of dihedral vanishes.
That's why increasing the vertical fin area can promote spiral instability-- because it reduces the tendency to sideslip while turning.
The tendency to sideslip while turning may be so slight as to be difficult to perceive, but it always there.
If you don't believe that the stabilizing effect of dihedral is dependent on sideslip-- if you are instead a believer in the (faulty) "projected area" theory-- then try using the rudder to command a slight amount of skid (rudder toward low wingtip, ball toward high wingtip), rather than slip, while banked and turning, while keeping the ailerons centered.  No matter how much dihedral your plane may have, it won't roll the plane back to wings-level if you are not allowing the plane to sideslip at least a little bit as it turns.

Area is held constant in the Lift Equation unless you change wing configuration in flight.

Lift = Air density × Wing Area × Lift Coefficient × Airspeed$^2$

Lift Coefficient is determined by airfoil type and Angle of Attack.
As we can see, only AoA and Airspeed are variable when determining Lift and Drag in a given working fluid (air, water).
Regarding the effect of area on the calculated result, we are saying (approximately, discounting wing root and tip effects) that Lift is directly proportional to an increase in span.  Changing chord would change the airfoil.
In real life, lift and drag are increased by lowering flaps, which increases Coefficient of Lift (therefor Lift).  This allows the plane to fly slower at the same AoA.

TY I guess I was thinking about how the dynamic pressure acts on the surrounding, say, rectangular control volume’s front control surface of which, as I would think to do, be the equal to that of the projected area.

@L T in ABQ yes, that would be sin angle x area.  At low deflections boundary layer/turbulence may be a factor too.  Deflecting a control surface can lead one to consider it and what it is attached to as one, and continue working the lift equation based on a new airfoil.  Works for reducing lift too (as a spoiler).


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Why are aircraft coloured in yellow during construction, repair or overhaul?

Why are aircraft usually coated with "yellow", while either during construction or repair and overhaul?
What exactly is the purpose of it?

Could you please provide the source of your image?

What type of plane is that?

The aircraft in the picture is Su-34

For unassembled and new planes or planes not yet painted the green/yellow color you see is the anti-corrosive coating on the aluminum

...every unpainted airplane is nominally green from being coated
  (typically) with an anti-corrosive green zinc chromate or zinc
  phosphate primer over the aluminum skins. The different shades of
  green simply tell you that different vendors produced the different
  pieces—they don’t all use the exact same primer.

Originally it was some variation on Zinc Chromate but it was found to be fairly toxic other things have been used over time which lead to the more green color and even some potentially "chrome-free" options.

do you mean nominally or normally?

@bogl: It's a quote from the given link. "Nominally" is in the original.

To add to this, in the US, you will typically see the trade name "Alodine", which is usually called out in drawings as something along the lines of "CHEM. CONVERSION COAT PER MIL-DTL-5541 , TYPE , CLASS ", where  is I for coatings with hexavalent chromium or II for coatings with no hexavalent chromium, and where  is 1A for maximum corrosion protection, painted or unpainted, or 3 where the corrosion protection needs to preserve electrical conductivity.

"nominally" would be the normal, expected word here, FWIW.

Lamp black is added to yellow zinc-chromate to make it resistant to UV light and increase wear resistance. This results in a green color. The more lamp black that is added, the greener the color.

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Is it safe to fly on airplane with lithium batteries in cargo hold?
Lithium-ion batteries have the tendency to go on fire.
I checked baggage policy of European low cost carriers (easyJet, Ryanair, WizzAir), and while spare batteries are banned from cargo hold, it seems that batteries in devices are allowed (also hand baggage could be placed in hold if there is no place in cabin).
If spare batteries are dangerous, aren't batteries in devices too?
A few incidents happended when lithium-ion battery exploded, and the fire has been extinguished by cabin crew.
Such fire could also happen in cargo hold. What's happens then? I've seen people question the ability of halon fire suppression systems to extinguish lithium battery fire, because it works by blocking oxygen from fire, while lithium-ion batteries do not need oxygen to burn:

Halon basically works by displacing the oxygen that is feeding the
  fire - and won't work when the material that is burning can provide
  its own oxidizer. Li-O batteries fall into that category, along with
  things like ammonium perchlorate (used to make solid rocket
  propellant), gunpowder, and oxygen generation canisters. Once ignited,
  they will continue to burn until the fuel is exhausted....
  (http://www.pprune.org/australia-new-zealand-pacific/538637-melbourne-airport-737-cargo-hold-fire-poss-due-lithium-ion-battery-2.html)

Also this:
https://batterybro.com/blogs/18650-wholesale-battery-reviews/19673027-plane-safety-systems-are-confirmed-to-not-stop-lithium-ion-battery-fires
On the other hand in comments to this question: What safety differences exist between carrying laptops in checked versus carry-on baggage? people suggest that it will keep fire from spreading until battery extinguishes on its own.
Moreover checked baggage is not always handled gently by airport employees, which can damage electronic devices - and batteries in them, which makes them more likely to catch fire.
For me it seems like any airplane carrying electronic devices could go on fire at any moment, and each flight is as safe as the batteries it carries. On the other hand aviation has stringent regulation about using electronic devices on board out of fear of interfering with airplane systems. I guess that if lithium batteries were so dangerous as I think then they would be banned from cargo hold.
So is airplane crash due to lithium battery fire a real danger, or do I worry too much?
(I guess I'm a little nervous - I'm going to fly a third time in my life so far.)

Related

As you mentioned, the danger is non-negligible. IMHO any potential fire in the cabin would be detected and handled much faster than in the cargo hold (I may be mistaken though). But people would not fly without their laptops or phones.. So appparently the benefit overweights the risk

@mins: Now think about hundreds of tons of kerosene in the tank
Yes, I know - TWA 800 comes to mind. Nothing is 100% safe. However I have more trust in something built by Boeing or Airbus with express purpose of flying.
Regarding batteries I think I feel uncomfortable because it seems to me that the risk is outsourced from aviation industry to some random battery producer. OK, most of them are problaby also reliable - batteries going boom are rare events - but there are so many battery types, cheap Chinese spares, and stories like Samsung Galaxy Note 7.

@TomMcW: The reason they are allowed installed in devices is that they are less likely to get damaged or shorted out while in the device
I once had a cell phone that worked and looked perfectly good from the outside (though the battery charge didn't last much). I opened it one day only to discover swollen battery.

@infrequentflyer Old batteries always swell. That's how you know it needs replaced. That doesn't mean it has become dangerous. But, older batteries are a bit less trustworthy. They slowly grow tiny dendrites which can cause a short if they reach across the insulating material. So if a battery off noticeably swelled don't charge it

You may be interested in Why is there so much fear surrounding LiPo batteries? on [electronics.se].

No, it is not safe to fly on an aircraft that has lithium-ion batteries in the hold.  There is a commentary on FAA Safety Alert for Operators (SAFO) 10017 here, which was issued after the crash of UPS Flight 6.
Admittedly, this was a bulk load of 81,000 batteries on a cargo flight.  However a search for 'battery' on AV Herald shows between one and two incidents each month, of lithium ion batteries/devices igniting in the cabin.  These are only the ones reported on that website, we don't know how many may go unreported
The ICAO also considers Li-ion batteries a risk but as Simon Hradecky points out, there is a conflict between this safety advice and the security requirements that force passengers to check-in laptops, tablets etc on some flights.
Personally, I think that, whatever the ICAO, FAA and airline requirements, there are going to be some of these devices that get into the hold (people will forget that they left a battery bank in a bag and security will not recognise it on the scanner). We know that they regularly catch fire.  There are almost certainly going to be airliners brought down by this, it may have already happened - the EgyptAir MS804 fire hasn't been explained yet.

there is a conflict between this safety advice and the security requirements that force passengers to check-in laptops, tablets etc on some flights.
The laptop ban seems to be limited to flights from US and UK to Middle East - as for as I know there is no such ban on flights between two European countries. On the other hand while you do not have to put your laptop in checked baggage you are apparently still permitted to do so. And it's not only electronic devices - lithium batteries seems to be everywhere these days, e.g. in torches, electric screwdrivers etc.

There is difference between 48,000 and 100 battaries. Anyway massive transportation is bad idea. But what about passanger's devices

@Евгений Новиков Since the beginning of May 2017, the following cabin fires due to passengers' devices have been reported: 2 August - Lufthansa Airbus A380-800, D-AIMI, (flight LH-440).
30 July - SriLankan Airlines Airbus A330-200, 4R-ALB,(flight UL-166).
22 July - United Airbus A319-100, N834UA, (flight UA-1536).
14 June - Germania Flug Airbus A321-200, HB-JOI, (flight GM-3225).
30 May - Jetblue Airbus A321-200, N967JT, (flight B6-915).
6 May - V-Air Airbus A321-200, B-22610, (flight ZV-252).

Lithium batteries do NOT produce oxygen. The problem with extinguishing them is that they do not NEED oxygen to produce heat. They produce heat through electrical discharge rather than combustion.
The reason they are allowed in the cargo hold only when installed in devices is that they are less likely to get damaged or shorted out while in the device. Loose spare batteries usually have their contacts exposed and can come in contact with something metal that shorts them out and can cause a fire. If there's a fire, better that it be in the cabin where it can be extinguished.
There's still a possibility for a battery in a device to catch fire in the cargo hold. There are limits to the size of batteries allowed on passenger aircraft. Larger than that size, or not installed in a device they must have the "cargo aircraft only" warning label on them did they won't be loaded into a passenger plane. The rationale behind fire suppression in the cargo hold is that a single battery by itself is not going to do enough damage to bring down a plane. But it can start other nearby materials on fire. The Halon fire suppression should keep the other material from catching fire by removing oxygen. That won't stop the thermal runaway in the battery, but if you can prevent the rest of the cargo from burning the battery will soon be completely discharged and stop producing heat.
They certainly aren't totally safe. They're pretty sure that's what started the fire that brought down UPS flight 6. That said, the UPS situation is a bit different than a passenger flight. The main cargo hold of a freighter is far too large for a fire suppression system. AFAIK only the haz mat container in the very front is required to have a fire suppression system. Cargo containers tend to be packed pretty tight, so the hope is that fires will run out of oxygen. This is certainly not always true as can be seen by UPS 6.
There is no way to eliminate every possible risk on an aircraft. But by taking the necessary steps the risk becomes very small. Lithium battery fires are reported often, so we need to be aware of the danger. But if you consider that there are thousands of flights every day and I'd bet that every single one of them for the last 10 years has has lithium batteries on board - usually multiple batteries - problems are extremely rare. I'm sure a lot more people have been killed by lithium battery fires at their homes than on a plane.

Li/LiPo battery explosions do involve oxygen. The primary oxidant is stored in the form of metal oxides in the cathode, but the free solvent electrolytes will react violently to oxygen in the air.

AIUI it all depends on quantity
It's not practical to totally eliminate the possibility of an ignition source in the cargo hold. Therefore the holds have fire suppression systems to keep any fires under control until the plane lands. The occasionally lithium ion battery mixed in with regular baggage won't prevent that.
OTOH a large shipment of lithium batteries can create a fire that burns very hot and is damn near impossible to put out. That is a serious hazard to the plane.

Li-ion battaries are safe if they isn't counterfeit
Battaries manufactoring is hi-tech process, and there is limited count of companies, that can make it. For example nanotechnology can be used while li-ion bataries manufactoring.
Each battery has own datasheet. This document contains techical information and information about tests.
Battaries testing
Consider typical datasheet of ICR-18650-26F battery, manufactored by Samsung SDI
It is safe to

Heat battery to 130°C for 60 minutes
Short-circuit by less than 50mΩ wire for 3hours
Drop full-charged battery from 1.5m 6 times
Overcharge with 12V and 2.6A for 2.5 hours
Vibrate between 10Hz and 55Hz with amplitude of 1.6mm
Reverse Charge with current 2.6A by –12V for 2.5 hours

Root of ban rules

In my opinion this bans based not on logic and statistics, but on fears and prejudjes.
But anyway if someone is seriously tuned, there is no problem
Counterfeit
This is a problem. There is no quality control on low-quality manufactories. Good news is that well-known electronics manufactorers don't use it.

Most of current fires on planes are due to the batteries of electronic cigarettes. It's great to know they are counterfeit, but this also means we need to take some action.

@mins e-cigs consume a lot of electric power. For IMR18650 it is ok, but for ICR not. This may be a problem. Also e-cigs have high temperature parts, and maybe they causes fire, not battery

"Li-ion battaries are safe if they isn't counterfeit": Not necessarily.

authors: Евгений Новиков

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What is an easy format for giving pilot reports?
Is there a technique anyone has to make it easier to give PIREPs (mnemonics, etc?)  I'd like to be able to give them while I fly but I can never find the expected format handy, so it ends up being a hassle.  If there's a trick anyone has to make it easy to give one, please share!

Who you are:
Cherokee 1234A, a P28A
Where you are:
10 miles north of La Belle VOR, altitude 6000 feet
Build your own "METAR":
Five minutes ago (time) wind aloft 230 @ 24 (wind) imc (visibility) medium turbulence (weather phenomena) broken clouds at my altitude, clear below (cloud cover) temperature 10 degrees (temperature)

That's it!
There might be a way to exactly meet the form the controller needs to write it down, but this works fine and you have a fluent and well structured report.

+1 for "Build your own METAR" - I never thought of doing it that way! This isn't exactly the order the information gets entered in, but it's a format Flight Watch / Flight Service / ATC will be familiar with and there's a good chance they'll be able to parse it quickly - worst case they may ask you to repeat a couple of the items.

PIREPs have no required format other than the identifying information: Location, Time, Altitude, and Aircraft Type.  Other than that, you can call in any number of weather elements as a PIREP.  I often call in nothing but winds aloft and temperature, simply because I know those are more difficult for the weather service to measure.
AOPA SkySpotter provides a nice flash card for recalling the various items, but there's no mnemonic provided.  If you're interested in giving the most complete PIREP possible, I'd suggest following the same format as an ATIS broadcast: wind, visibility, clouds, precip, and then touching on any other relevant information such as temperature or turbulence.
All in all, though, the most important thing about PIREPs is that you give them. The briefer or controller who takes your report will be able to format it properly if you give the elements out of order...they're just happy to get it at all.

I'll echo that the most important thing about PIREPS is that you give them (especially for winds / icing / turbulence differing from the forecast - that stuff can make it into the next pilot's briefing and save someone a lot of grief!). If you give them in the order on the SkySpotter form it's nice for the person punching it in because that's the order they're used to seeing it in, but they can generally sort things out and will ask you for missing information if they think it's important.

@voretaq7 With all of the automated wind collection (real time doppler and automatically reporting airliners), wind pireps aren't really all that important anymore.  The other information is though!

The skyspotter card is great, just keep it in your kneeboard our somewhere handy until you need it!

@lnafziger more than once I've had winds significantly different from forecast (like "the winds are 180 degrees off from what the briefer said") which is something worth reporting. Generally you're right though: the winds are pretty accurate & I just say "winds as forecast"

The technique I have is to just call up ATC and ask if they've got time for "a quick PIREP". If I'm giving a PIREP I'm almost always either on flight following or IFR, in which case they already have my aircraft type; from there, I give a brief report with the items I want to provide. It usually looks something like this:

Cessna 321AB: Seattle Center, Cessna 321AB... I've got a PIREP for you if you have a moment.
ZSE: Cessna 1AB, go ahead.
Cessna 321AB: Ok... over CLM at 7500, five minutes ago, the winds aloft were 280 at 20, temperature 39, clear below.
ZSE: Cessna 1AB, got it. Thank you.

I never worry about order, and I've never gotten yelled at by ATC or Flight Service.

As an aside, if it's crazy windy aloft with lots of changes per altitude, I'll give ATC winds almost always. If there's icing conditions or below-freezing temps, I will always provide a PIREP. They don't get into the system often enough and if you treat it casually and provide just the relevant info for the day (if it's clear, don't tell them this) you're doing everybody a great service.

I'm under the impression you shouldn't call Center with PIREPS.  I think it be better to call Seattle Radio on 122.6 in the vicinity of CLM?

@abelenky generally when IFR it's better to stay on frequency. Seattle Center, particularly during cruise, often has more free time than Seattle Radio anyway. If you've got something from the AIM that recommends FSS as the one place to report pireps, I'm all ears! :)

I guess the difference is that I'm VFR, and therefore rarely talk to Center except for Flight Following.

Yeah, seems reasonable. Honestly, in most cases ATC is pretty willing to help out, including jotting down PIREPs, unless they're slammed or having a bad day.


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Are there types of instrument approaches besides precision and non-precision?
In the 1990s there used to be two basic types of instrument approaches: precision and non-precision. How many different kinds are there now, and what are the differences.

I'm not sure what you mean by "type", could you explain a bit more about what you're asking? The FAA Instrument Procedures Handbook uses the word "type" to mean ILS, LOC, RNAV, contact, visual, PAR, ASR etc. but listing and comparing all of them would need a very long answer.

@Pondlife Poor choice of a word on my part, but I couldn't offhand think of a better at the time of posting. Now that I think about it again, I perhaps should have used "categories". What I was trying to find out, and what tmptplayer admirably answered, was whether the two "basic types" (as I chose to call them) were still thought of that way and how much things have changed in the 15 years since I've done any IFR flying.

All approaches can still be categorized as a precision or non-precision.  Some of the terminology has changed, radar approaches are becoming less common and and GPS approaches are becoming more common, but the fundamentals are the same.  Precision approaches still provide glideslope guidance, and non-precision approaches do not.
It may be important to note that many flight computers blur the lines some with GPS approaches.  There are approaches where the plate still calls the bottom altitude an 'MDA' (instead of 'DH' or 'DA') as you would in a normal non-precision approach, but the flight computer will generate a custom glide slope to that point.  Because this is generated artificially inside your aircraft and not schematically planned by a certified official, this still only qualifies as non-precision.
All in all, if you're trying to pick up instrument flying after a long break, you'll still be good to go with your basic understanding of precision versus non-precision approaches.

Still non-precision on the non-official glide slopes for good reason.  You can follow it, but have to monitor it as it may mislead you.  I ran across one that would have put me below MDA had I followed it.  Had to level off for about 30 seconds, then pick it up again to be legal.

@Brian You're absolutely right Brian - there are many traps in the intermediate descents for non-precision approaches which may be driven by obstacles/terrain that make a constant gradient descent unsafe.  I would never endorse following a FMS generated glide slope that violates the actual approach - you must always be cognizant of the restrictions.

The FAA now issues Operations Specification C052 (Straight-in Non-Precision, APV, and Category I Precision Approach and Landing Minima - All Airports) to Part 135 (and probably very similar for Part 121) air carriers.
In that Ops Spec, they list three categories of approaches:

Nonprecision Approach Procedures Without Vertical Guidance
Approaches With Vertical Guidance (APV), and
Precision Approach Procedures (ILS, MLS, & GLS)

The basic difference between the categories is whether or not you have vertical guidance that can be used for the approach and the degree of accuracy provided by the underlying navaid.
There are also some Flight Management Systems (FMS's) which calculate the vertical navigation (VNAV) component for nonprecision approaches that would not otherwise have it.  These "pseudo-glideslopes" are for reference only and the pilot is responsible for verifying that all crossing restrictions are still made.


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Ground effect and Lift coefficient
Is there a correlation between the lift coefficient and the proximity between the wing and the ground? I know that the lift coefficient is dependent on angle of attack; However, based on experiments that I have conducted, the results disproved the claim somehow, at the same angle of attack (0 degrees), the lift generated is higher when in ground effect than out of ground effect. Based on the experiment, given that wind velocity, wing span and density (according to the ISA) is the same, does this meant that ground effect (proximity when in ground effect) can bring a change in lift coefficient? Moreover, is there a specific correlation,is it linear or exponential?
It is really weird how I can find literally anything but the correlation between proximity and lift (or lift coefficient), there are essay on how ground effect affects forward swept wing aircraft, and yet there's not a single essay about proximity and lift coefficient :(

Graph from https://www.faatest.com/books/FLT/Chapter17/GroundEffect.htm

My collected data

According to Youtube, the lift is exponential to proximity when in ground effect

What is the source of your graphs?  ANA?  Should include citation in question.

I've learned, that a wing in ground effect behaves like having a higher aspect ratio. So i would guess this increase in cl-slope comes from higher virtual aspect ratio. But it is just a guess.

@JVAV_master what type of airfoil did you use?  What do your results "disprove"?

"the lift generated is higher when in ground effect than out of ground effect" is pretty much the definition of ground effect.

Haven't you answered yourself? The second graph clearly shows that yes, the lift coefficient increases in ground effect, and importantly, its derivative also increases (i.e. lift grows quicker with AoA). What is so surprising here?

As mentioned in this excellent answer, ground effect of aeroplanes can be modelled as extra lift from the mirror image of the plane. The image above depicts the effect on the tail plane, main wing is identical.
This Prandtl Lifting Line Theory can be explained as extra lift from the mirror image of the wing. Torenbeek Appendix G.7 contains some expansion of the ground effect with flaps extended, with three diagrams on its effect on airfoil lift, below.

Graph b. shows the two lift slopes of a wing in and out of ground effect. For a given angle-of-attack $\alpha$, there is indeed a higher $C_L$ in ground effect.

I submit there is higher Lift for a given AoA.  Coefficient of lift is AoA (and airfoil type).  Could your "mirror image" also be the lower wing of a biplane?  It is said most of the lift is from the upper wing but ...

Setting the "experiment" aside for now, we can see that ground effect does indeed increase Lift.  The first picture of the excellent reference Chapter 17 Ground Effect tells much.  As one our most prominent writers often tells us, the vortex rolls off the entire trailing edge, not just at the wing tips.
Further reading compares ground effect (on induced drag) at 1 span length, 1/4 span length and 1/10th span length.  1/10th span length lowered induced drag by over 40%!
Reasons for this may lie beyond "coefficient of lift", which deals with airfoil type and Angle of Attack.
From the first picture, we can see downwash is reduced.  From the graphs, stall (of the upper wing) occurs at lower AoA.  This implies weakened circulation over the top of the wing, resulting in earlier flow separation.  This would seem to make ground effect bad but ...
Greater lift is generated by increased air density underneath the wing.  This is not unlike the phenomena of "water skiing" where the (much) greater density of water can hold up the entire weight of a person at less than 20 knots.  Water skis are not know for their top lift.
There is also the thought that ground effect extends wingtip vortices away from the wingtip.
In summary, increased air density under the wing allows the plane to maintain lift at a lower AOA.  Combined with reduced wing tip vortex drag, induced drag decreases as ground proximity increases.

So is the increased air density under the wing a factor of the change in lift coefficient? Since I was thinking of using the ISA density at sea level to calculate the lift coefficient of the experiment.

JVAV_master well, technically, density Rho is considered separately in the Lift Equation, but you're on the right track.

Robert, at clearly subsonic speeds density changes very little, it is pressure that is increased on the lower side.

From PV=nRT one can express higher pressure from higher density.
Certainly not comparable in strength to a shockwave, but over the entire bottom of the wing.

well with the experiment the wind speed is roughly around 3.4m/s, which is pretty slow but still works for a smaller model.

JVAV_master what you may want to do is build your graph at various AoA, including at least one negative one.  Try to find the AoA where your model generates 0 lift.

Robert DiGiovanni Yes I've plotted a AOA to lift graph with different curves representing different proximity, it has been uploaded onto my post

Ground effect is complicated. That is because it actually consists of at least two effects, subsumed under a single term:

The wake cannot continue downwards past the wing, so it is deformed when the ground blocks it, and
Air flow on the lower side of the wing is partially blocked.

The first effect depends on the height of the wing relative to wingspan and the second one on the height of the trailing edge relative to wing chord. Therefore, plotting all effects over one single parameter will only be valid for a narrow range of conditions, and omitting those makes the graph worthless.
Take angle of attack (AoA): At low AoA, the lift curve slope is higher than in free flow while at high angle of attack it becomes lower. Hing AoA means also high induced angles, so here the blocking effect of the wake by the ground becomes more pronounced and reduces induced effects. To say that "ground effect increases lift curve slope" is only valid for low AoA.
Next, AoA is based on the definition of the wing reference chord. It does not include the lift provided by camber, neither does it make clear how twist, changes in airfoils, flap deflections and washout change the local lift over span. Only when that information is included can ground effect be described properly.
Or look at how height is measured. Is that the height of the leading edge, or the quarter chord line or the trailing edge? Some authors even omit that distinction and seem to think it doesn't matter how height relative to the ground is defined. This also makes their graphs effectively worthless.
And then there are authors who present their results without labels or legends. Your question is testament to you being part of this distinct group. I am sorry to say that this makes your graph worthless as well.

Can you give me adivse what to do now?  Unfortunately I found out to late my diagram is not airfoil section of wing it is CDGE(chord-dominated ground effect) test for airfoil in wind tunnel , so all my question doesnt make sense, because airfoil dont have 3D effects. So can I use this "2D" pressure distribution for wing or it is completly different? https://aviation.stackexchange.com/questions/96059/is-effective-aoa-increased-at-wing-in-ground-effect

@JurgenM Depends on the aspect ratio of the wing. The diagram explains well what happens away from the wingtip, and the higher the aspect ratio, the more of the wing is "away from the wingtip". I find the diagram very helpful and illustrative. It also shows how important the distance between trailing edge and ground is. Or is h a different parameter? You should explain better what the symbols and axes show, then the question does make sense and is useful.

OK thanks for help. Yes h is changing and c is fixed. I will edit this in text. But I think is not correct ask members "if decrease in downwash increase eff. AoA.." if diagram show airfoil(2D), because downwash/eff. AoA is related to wing,3D effects..The goal of question is find out is wing really feel effective AoA in reality caused by downwash or this just mathematical manipulation  how explain change in lift with numbers..

@JurgenM You get high pressure below the wing if the gap between trailing edge and ground is small. Increasing AoA doesn't change this much beyond a few degrees. The high pressure forces more air to flow over the wing, so at low AoA the local flow angle at the nose if higher, but doesn't increase much with increasing AoA - the pressure will not rise linearly, after all. So at low AoA lift is higher but at high AoA it grows only slowly, compared to free flow. It's actually quite simple - just look at how the molecules will behave and forget the wake.

"The diagram explains well what happens away from the wingtip, and the higher the aspect ratio, the more of the wing is "away from the wingtip" higher the aspect ratio of airfoil in wind tunnel=more show  2D airfoil and less  show real 3d wing pressure distribution?

@JurgenM An aspect ratio is something a wing has, not an airfoil. There is no "aspect ratio of airfoil".

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
If absolutely nothing changes except temperature, does indicated altitude increase, decrease, or stay the same?
I have gotten conflicting answers from CFI's on this one. In bold are the only things that changed or would potentially change.
Initially:
Aircraft is parked at a very dry (to factor out humidity) airfield

Field elevation of 0 ft
Local altimeter setting is 29.92
Temperature is 15 C
29.92 in the Kollsman window
Indicated altitude is 0 ft

Later:
Aircraft is parked at same very dry (to factor out humidity) airfield

Field elevation of 0 ft
Local altimeter setting is 29.92
Temperature is 40 C
29.92 in the Kollsman window
Indicated altitude is ? ft

I know the density altitude increased. I know the pressure altitude remained the same. However I would like to know if the indicated altitude is greater than 0 ft, less than 0 ft, or 0 ft.
I have seen diagrams online that try to explain this concept but confusingly enough, change both true altitude and temperature in their explanations. I am keeping true altitude constant here to get to the bottom of it.

Robert, I have seen others on stack exchange say this is correct: link and it shows that in warm conditions, indicated altitude reports lower than true. What say you?

If "absolutely nothing changes", then pressure doesn't change, then pressure altitude doesn't change by definition. QED. (If we ignore thermal expansion of the internal components of the altimeter, but it is generally unpredictable how this would affect indication).

Pressure is a measure of the mass (weight) of air above you. If the only change is that the temperature increases, then the column of air above you is taller (air will expand), but it still masses (and weighs) the same.

Charles Bretana, your answer implies that temperature change given constant pressure does not change the indicated altitude. but this link seems to say that it does. It appears to say warmer conditions make indicated altitude report lower than true, given constant pressure. What am I missing?

What you are missing is that when you are given an airport altimeter setting, it takes into account ALL variables and your altimeter will read correctly for the airport you are at.

Altimeters are "told" what the pressure is at MSL.  They then apply a model of the pressure above that point to map to altitude.  The model assumes standard temperature.  The model becomes less correct as temperature deviates from standard.
Because your scenario has the plane at a MSL field and the altimeter is set properly for MSL, the indicated altitude will be 0.
For actual altitudes above MSL, but with temperatures above standard, the altimeter will indicate an altitude below the true altitude.
Note that most materials assume you are flying and want to get the true altitude from your indicated.  Your question is in the reverse where you want to get the indicated from a known true.  On a hot day, indicated elevation is less than true elevation for altitudes above the reference location (which is normally 0MSL).

So if you went from parked at a 1000' airport, 29.92 reported and in the window, 13 degrees (ISA for that altitude) and 1000' indicated to: 1000' airport, 29.92 reported and in the window, 40 degrees, there would be a change in the indicated altitude? If so, I regret posing my initial question at 0'.

@user59676, Right.  0MSL is special because that's the reference.   For fields above that, the indicated altitude should be lower when the temperature rises but the altimeter is properly set.

So just so I understand your stance, 757toga. In my scenario posed in these comments, is your answer less than, more than or equal to 1000' on the indicated?

Interestingly enough, the FAA needed to put out guidance on this issue you are trying to get to the bottom of.
Here is the scenario.  You are flying on a fixed glidepath to the runway.  You are exactly in the middle of the localizer and glideslope signal.  To put things into perspective, these signals do not change with atmospheric conditions.  A glideslope bean will put the aircraft at the same true altitude every single day.
On ILS approaches with quite a few stepdown procedures, the requirements is to remain at or above the MEA for each segment until the final approach fix at which time you will descend on the glideslope to the runway.
Quite a few pilots will capture this glideslope at an altitude higher that what the published altitude is at the final approach fix.
Here is the jist of the InFo from the FAA.  In cold than normal weather, those pilots who capture the glideslope high will most likely remain at or above the MEAs for those intermediate segments.  IAF --> stepdown --> stepdown --> PFAF.
In warmer than normal weather, the same pilot will most likely descend below the MEA for those segments and could cause traffic issues for other aircraft.
https://www.faa.gov/other_visit/aviation_industry/airline_operators/airline_safety/info/all_infos/media/2011/InFO11009.pdf
The saying "FROM HIGH TO LOW... LOOK OUT BELOW" is true for both pressure and temperature.

The METAR for the airport will automatically compensate for the temperature differences through its use of the altimeter setting.  Remember, the altimeter setting is representing the altitude you would be at above sea level.
A really good example of this is in Colorado.  Today, the METARS look like this.

Wilkerson Pass (Elev. 11,259 FT) - K4BM 132135Z AUTO 17005KT 10SM SCT032 SCT038 BKN120 12/05 A3077 RMK AO2 LTG DSNT NE

Red Cliff Pass (Elev. 12,047 FT) - KCCU 132135Z AUTO 11013KT 10SM SCT037 SCT055 BKN080 18/04 A3078 RMK AO2

La Veta Pass (Elev. 10,124 FT) - KVTP 132135Z AUTO 10010G14KT 10SM SCT025 SCT034 SCT039 17/08 A3064 RMK AO2

Alamosa Airport (Elev. 7,542 FT) - KALS 132152Z AUTO 11013G25KT 10SM CLR 28/06 A3038 RMK AO2 PK WND 11027/2126 SLP182 T02830061

Colorado Springs Airport (Elev. 6,187 FT) - KCOS 132054Z 14011G18KT 10SM SCT070 SCT250 28/08 A3038 RMK AO2 SLP195 T02830083 56009

Gunnison Airport (Elev. 7,667 FT)- KGUC 132127Z AUTO 08016KT 10SM -RA SCT080 OVC100 22/08 A3042 RMK AO2 PK WND 12029/2105 LTG DSNT E AND SE TSE16RAB24 PRESRR P0000

I have tried to show passes and airport close to each other to preclude the possibility or an airmass or pressure change.
Look at those altimeter settings.  They are corrected for the non-standard temperatures to show true altitude at their locations.  The altimeter setting must be higher in the passes because it is warmer than standard today in Colorado.  If you look at these airports in the winter, you may find the altimeter settings are lower than the corresponding airports.
The elevations listed are for the weather station and not the airport elevation as found in the chart supplements.
https://aviationweather.gov/adds/dataserver_current/httpparam?dataSource=metars&requestType=retrieve&format=xml&stationString=K4BM%20KCCU%20KVTP%20KALS%20KCOS%20KGUC&hoursBeforeNow=1

LADLE is only for localizer minimums.  Why would you use it on an ILS?  TERPS requires there are no waypoints from the PFAF to the MAP on a ILS.   This is why FMS's don't show waypoints inside the FAF.

I see your point.  I agree with you.  I looked for such a note and could not find one.  This would be a good thing to report to the FAA.

https://www.faa.gov/air_traffic/flight_info/aeronav/aero_data/Aeronautical_Inquiries/

The FAA is removing all "LOC ONLY" notes on waypoints inside the PFAF.  They are instead putting in verbiage in the AIM and making it clear in the front of the TPP that those waypoints do not apply to ILS procedures.  I asked... they answered.

Altimeters work by comparing static air pressure on a sealed metal bellows.
Further research has shown that the bellows is evacuated to eliminate temperature effects and only reads air pressure by measuring the distortion of the metal. If you put the altimeter in an oven (with a venting port) and raised its temperature from 15 C to 40 C, it should read the same altitude!   (Question answered right there.)
Above the ground, altitude errors can be introduced by changing barometric pressure caused by highs and lows as well as non standard lapse rates using ground readings as references.
With this particular question, flying locally with temperatures rising from 15 C to 40 C, above the ground the altimeter will read lower than true altitude.  But, upon landing, it will read: 0 feet at 29.92.

There are ways to compensate for metal expansion or contraction due to changing temperatures.  Altimeters are not unlike precision watches.

Yes, it is essentially the same as a mercury baro, it only measures pressure.  That really brings the hot and cold "vertical columns" of air in focus as sources of error.

An altimeter setting of 29.92 at such airfield (0 ft elevation) means that the air above such airfield, weights the same as a column of mercury of 29.92 inches. The altimeter reads the relative weight of the air above the aircraft compared to the setting (29.92.) Because of the fact that we can assume that the air weights the same in the vicinity of the airfield, the parked aircraft will also read 0 ft. The 29.92 inHg reading is called barometric pressure.
If the temperature rises and the altimeter setting stays constant (barometric pressure constant), the air expands reducing its density so the airfield will report a higher density altitude. A higher density altitude means that the aircraft's performance will be such as if it was at a higher altitude. Human performance is also altered, for example if the density altitude is 2000 ft higher compared to the standard atmosphere and you are travelling in a non pressurized cabin, you will start to experience hypoxia 2000 ft lower compared to the standard atmosphere.

I share the ops questions, and I don't feel it's been fully answered yet.
If you are flying through air at a constant pressure with the altimeter set properly, at standard temperature, then indicated is showing height above that altimeter setting, which could be 29.92, standard datum plane, or some other setting which is assumed to be mean sea level.  Thus indicated shows MSL.
Now as you fly and maintain indicated altitude, you fly into colder air.
The rote rule, which I'm fine with, is that indicated will stay the same, but MSL will be lower.  high to low, look out below.
Just how can you possibly be lower, if the altimeter itself didn't change?  In this case, it must start to trend down slightly, so you follow it, thinking you are still at the same MSL altitude because it's still indicated, but you're actually lower.
After all nothing else changed, but temperature, and the airplane is flown at a lower MSL than indicated.
Looking at the inverse, say you stayed at the same true altitude (somehow, using a different instrument), then the altimeter would trend down, but you wouldn't follow it, and it would thus show it's errors.
Perhaps the problem we're having is trying to mix high to low, low to high concepts with density altitude concepts.   I would be happy if this was true - the altimeter changes a little bit with temperature, it tries to ignore it, but doesn't completely do so.  And we as pilots much understand this.
But density altitude is a calculation that is not at all trying to ignore the temperature's effect on altitude.  If altimeters did account for temperature, they'd show you density altitude.   And you'd have great insight into your aircraft's performance in real time, but you'd have no real clue what your true altitude is.
So calculated density altitudes at one spot are going to be possibly much different than the muted indicated errors on that same spot.  But, the errors and density altitude will move in the same direction.
Please feel free to reset my thinking, if it's way off.

Fair enough, but since they are related through temperature, I was hoping that thinking of them together would help make sense of the ops question.


text:
Are there any gliders that can fly over the Himalayas?
Do gliders (sailplanes) use ridge and wave lift in the Himalayas to go to extreme altitudes, possibly above Everest's peak?

Here is a link answering my question, provided by user mins but the comment has been deleted in the meantime. https://www.adventurealternative.com/destinations/nepal/himalayan-glider-flight/

Do gliders (sailplanes) use ridge and wave lift in the Himalayas to go to extreme altitudes, possibly above Everest's peak?
Yes, there are gliders touring Himalayan peaks over 8,000m, including Annapurna and Everest, using mountain waves. Montain waves differ from ridge waves as they are created on the leeward side of the mountain. They can be flown without being close to the relief.
Gliders over Himalayas
Example with this Stemme S10VT motorglider:

The image is extracted from an advertising page of the company doing this business. The glider has a service ceiling of 9,140m. Flight is done with oxygen masks in a non pressurized cockpit.
Video on Youtube. From the video:

Mountain waves
These flights are linked to the Mountain-Wave-Project, initiated by René Heise and Klaus Ohlmann, both glider pilots, the latter was the first pilot to glide over Everest. Mountain waves are air layers trying to stabilize after they are disturbed by relief:

producing these beautiful lenticular clouds:

Lenticular clouds over Alps, source
Stratospheric mountain waves
Mountain waves are a strong lift source. Using stratospheric mountain waves, Airbus reached 23 km with two pilots onboard a Windward Performance Perlan II, surpassing U2 record*:

Airbus Perlan II mission, source
Absolute altitude versus height gain
Flying at high altitude is not the biggest problem for a glider. You may start a bit below, gain a few altitude, and claim 6,000 m or 8,000 m. Any commercial airliner is able to glide from its cruise level, about 10-11 km. This is not soaring, that is using wind to gain altitude.
Gaining altitude requires specific skills, a good knowledge of winds, a favorable location and a great deal of cooperation from the weather. Not all gliders are equal, those made for high altitude may fly poorly at low altitude. There are glider categories to file a record at FAI because performances depend on the wingspan to extract lift.

The record for gain of height is 12.9 km. It was set in 1961 and, according to Wikipedia never outdone in 60 years.

In contrast altitude records were set over years, and Perlan II was able to fly at 23.2 km in 2018, but the glider was towed up to 12.2 km (40,000 ft) by a turboprop aircraft (tow release video) and from the narrative of the flight, there was no way (in this particular instance) to reach 12 km without being towed.

*Humor. U-2 record is here.

Just for clarification: 9140 m are 30,000 ft and 23 km are 75,500 ft.

This should be no problem at all. Even in the UK, where the highest mountain is about 4400 ft, the altitude record for a glider using ridge and wave lift is 32,000 ft.

Wow I thought there was only going to be a pithy answer of "yes, the space shuttle"

@llama while it may technically qualify as a glider on descent, highly polished bricks falling with style aren't really what most people have in mind when they think of gliders.  And in any event, the shuttle had essentially zero chance of ever gliding over the Himalayas; except for the remote possibility of an emergency landing the Shuttle always would reenter the atmosphere thousands of km farther East.

@llama A sailplane flies on thermal, ridge and wave lifts. The shuttle is no sailplane.

This answer is missing to mention the fact that any glider can fly at those heights. For decades the height record was at 15,000 metres (50,000ft) on a Grob G102 Std, a trainer glider. Way way higher than Everest. The big issue with flying at extreme heights is the need of more sophisticated oxygen equipment, the cold, and the coffin corner.

@MartinArgerami Not to mention the difficulty of eating, drinking and going to the lavatory in a comparatively cramped cockpit during the long period of time required for the ascent!

The most surprising fact is that it seems that you can glide over the Everest without being intercepted by Chinese fighters.

@Pere, perhaps they glide over Nepal, a sovereign state, rather than over Tibet, a Chinese region.

@mins - Yes, I might be understanding "over the Everest" (and over other border peaks mentioned in their web) in a too literal way.

@mins: yes, it's well known. He released at 12500ft.

@mins: and any normal glider can fly at those heights, if they somehow deal with the usual problems (cold and lack of oxygen). Which glider do you know that is not capable of flying that high, and why?

@mins: I don't know who wrote that in the Wikipedia article, but they have no idea what they are talking about. Here you have footage of a DG400 flying at 33,000ft, and there are higher flights. The height record before Harris' was by Paul Bikle, in a Schweizer 1-23E; any modern glider is insanely better than that. I have personally flown a Jantar Std at 27,500, and I have also personally seen many gliders flying higher than that. As for reaching the next wave, that has nothing to do with "ceiling", and all with pilot and weather.


text:
What can be done when the magnetic compass breaks during a cross country flight?
On United state a VFR cross country flight, after arriving you discover that the magnetic compass has leaked all of the fluid and is inoperative.
The weather at airport shows a fast moving cold front has just passed the night before. The winds aloft at 3000 feet and up were forecast to be very strong an the surface winds were forecast to be calm. The briefer also said that the pressure was falling rapidly. The ATIS/AWOS stated the winds as 270 at 15 kt. When you arrived at the airport, the wind sock showed the wind from the east at the arrival end of the runway you were planning to use.
What can you do?

Welcome to Aviation.SE! Are you asking if it is legal to takeoff and continue your cross country flights? If so, please add a country/regulation tag (e.g. [faa-regulations]) since legality might differ.

I vote to close as this question is disjointed and lacks clarity.

The title question is clear enough, but the scenario based narrative in the body is a bit distracting.  (the windsock is as irrelevant to the question as the milkshake is to the answer!)  It boils down to required equipment for VFR/IFR flight, and nothing more.  Which wouldn't be a bad question in itself, but easily searchable info...

Just as a practical matter, how often do you consult the magnetic compass when flying VFR?  I'm almost always flying by reference to terrain.

Since the question is "What can you do?", not "What can you do to remain in compliance with regulations", the best answer would be "you can just go fly".  Much of the US is covered by an east-west north-south road grid system anyway.  Just don't forget to look out the windows now and then.  If that seems like too much of a handful, perhaps you might want to bring along a hand-held gps unit.  Or your smart phone- just use google maps.

If you're in the United States and your airplane has a standard airworthiness certificate, you can go to the airport restaurant and order a milkshake while you wait for your magnetic compass to be fixed, since it's required equipment under 14 CFR 91.205:

(b) Visual-flight rules (day). For VFR flight during the day, the following instruments and equipment are required: [...]

Magnetic direction indicator.

You may want to check the ATIS before deciding on a milkshake or hot chocolate.

...It's a trap!

Is the pilot vaccinated


text:
What are the physical laws for upscaling an RC model to 1:1?
What are the laws of physics for upscaling an RC model from a smaller to larger scale or even to a full sized 1:1 aircraft? I guess the basic thing may be lift/weight ratio which was nicely described here:

... when you scale an airfoil up, the lift it produces increases with
  its area, which grows with the second power of size, but its weight
  increases with volume, which grows with the third power of size.

The above means the lift/weight ratio is worse for bigger vehicles which I guess makes them fly worse (less range, higher fuel consumption).
Are there any more laws to be taken into account for such upscaling? I mean in terms of aerodynamics or power source (battery/fuel) etc. Does the air behave differently with scale? Do different laws apply for different aircraft types (plane, helicopter, quadcopter etc.)?

Well, when you scale it up more, you can do less and less of the "tricks" RC planes can do.

When i see "law" i first think of regulation. Physics maybe the thing. Just my humble opinion though :) good question anyway

Related: http://aviation.stackexchange.com/questions/21646/why-cant-model-aircraft-be-used-to-discover-spin-and-stall-behavior-of-manned-a

And be sure to look at this one, too

http://www.aerotelemetry.com/press-design-news-airplanes-aviator

I found somewhat related post: Is there a maximum possible size for an airplane?

Interesting pub from NASA: http://www.nasa.gov/connect/ebooks/aero_modeling_flight_detail.html

This is not a full answer: much is mentioned by Michel Touw, but I'd like to correct a common misconception.
The mass growing as the third power of linear dimensions applies only to solid objects. But the airplane is not solid; rather, it's a thin-skinned frame. (Unless it's a solid foam RC model). Therefore, its mass should grow with the area, as the square of length.
However, this is, of course, not quite true. In reality, you need thicker skin, thicker spars, etc., and these elements will get heavier 'properly' with the cube of length - and even more, because they'll need to support themselves as well, with their added mass.
In the end, the mass of airplanes grows between the second and third power, and much closer to second.
Let's take B734 and B772 for example, which differ close to twice in linear size. Their empty weight (roughly 33 and 140 tons, depending on modification) differs by 4.25 times, which is approx. 22.1. MTOW has a similar ratio: 68 vs 300 tons, 22.15.

A lot of things happen, depending from what perspective you look at it. I'll first start with some scaling laws. Note that ~ means 'scales with' or 'is proportional to'.
Basic scaling laws:
Lets start with:
(1) length   ~    length
(2) density  ~    1 (is constant)

From (1) we can derive that:
(3) area     ~    length^2
(4) volume   ~    length^3

From (2) and (4) we can derive that:
(5) mass     ~    length^3

We also know that accelerations on an object don't change (example: gravity):
(6) acceleration ~ 1

Since force = mass * acceleration, from(5) and (6):
(7) force  ~    length^3

Since acceleration is contant (and here it may get a little weird):
(8) time   ~    sqrt(length)

From (1) and (8):
(9) velocity  ~  sqrt(length)

The idea from time may more comprehensible when you look at vibrating stick: a very long stick will have a longer oscillation period than a short one.
Aerodynamics
Now for the aerodynamics. As the length scale increases, to keep everything the same (proportional) the plane will also have to fly faster (by the sqrt of the length scale). This can also be seen from the lift equation:
L = C_L * 0.5 * rho * V^2 * S
L = W, for which holds that W and L (forces)  ~ length^3
length^3 ~ 1 (from C_L) * 1 (from 0.5) * 1 (from rho (density)) * V^2 * length^2
V^2 ~ length
V ~ sqrt(length)

The increase in both length and velocity increase something called the Reynoldsnumber, which is equal to:
Re = (rho*V*x)/mu  where:
    rho = density of medium (air)
    V = velocity
    x = characteristic distance
    mu = viscosity of the medium

As the Reynoldsnumber increase, in general the drag gets lower for a given amount of lift. This also allows (for most airfoils) a larger maximum lift coëfficiënt (the lift per area generated at a certain velocity and density).
Also your Mach number increases, since velocity increases.
M = V/a where
    V is the velocity of the aircraft
    a is the speed of sound

As M > 0.3 you have to take this effect into account. It decreases your lift coëfficiënt. However 0.3M is around 100 m/s, and your craft probably won't fly at that speed. At 0.3M the error is about 5%.
These are the 2 main aerodynamic factors that come into play. Note that both numbers are dimensionless.
Other factors
You can also think of other factors such as the range on your transmitter, structural changes in proportions. Controlability: as time increases with length, your craft will feel less agile, requiring longer approaches which may be out of sight.
But I seemed you wanted to know mainly about the aerodynamics. With the basic scaling laws, you will be able to derive what happens with most other factors you encounter.

Before reading this answer I wondered if the viscosity of the air would be a factor. I don't think I saw anything about properties of the air in your answer. Are the (fixed) properties of the air a factor in scaling?

No, the fixed properties of air don't change the scaling. Just like density doesn't scale. The velocity of the flow however, does affect the scaling as can be seen in the answer.

Could you maybe use some mathjax to make the equations a little more readable?

@ToddWilcox, viscosity is a factor. It's part of the Reynolds number. The Re number is the ratio of the mass vs viscous properties of the fluid. And because Re for airplanes is large (thousands to millions), it basically shows that aerodynamic forces are produced mostly by pushing masses of air around rather than by 'shearing' it. And thus you see air density (rho) in every equation.

You may want to have a look at the free NASA publication which explains the relationship between models and actual aircraft.
http://www.nasa.gov/connect/ebooks/aero_modeling_flight_detail.html

See Your answer is in another castle: when is an answer not an answer? on [meta.se] for why this is not an answer.

The stuff from NASA is a great publication - thanks for posting! :)

Thanks for the helpful advice on my answer. NASA has some great publications, your'e welcome.


text:
How can the range of an aircraft be calculated given real wind conditions?
I am very new to aviation and trying to understand how to calculate the actual range of an aircraft given real world wind conditions.  I understand from this related question that you need  30 minutes of reserve and that tailwind and headwind direction will obviously impact your range.  I've also heard that the altitude you fly at can impact your range because higher air is thinner and allows you to travel faster.  I also would assume that the aircraft load would impact range.  So my question is:
Given the theoretical range of an aircraft (i.e. from specs published at this site) how do you calculate how far the aircraft can actually travel at a given altitude, with a given load, and with current wind conditions?

See Ground Studies for Pilots, Flight Planning by Peter J. Swatton, Chapter 5, General Fuel Requirements - p. 110 and 6, 7, or 8 depending on the type of engines.

The "theoretical range of an aircraft" has a lot of "it depends" factors that are assumed in computing it, and how far you can "actually travel" has a similar number of factors that go in -- some are current conditions, others are things like planned altitude, how much reserves are required (driven by what rules you're operating under), etc.   Getting from the theoretical number to the real one would require reverse engineering all the assumptions from what they planned on, back out to what you're actually doing.  Best bet, as Peter Kampf says, is to do the computations from source documents.

The best answer: Use the charts in the respective Pilot's Operating Handbook (POH). There you should find correction factors for the parameters which influence aircraft range

Fuel on board: The more, the better. But note that doubling fuel will not double range.
Take-off mass: If you take no payload, the aircraft will produce less induced drag and reach a slightly higher range. See the chart below for an example.
Wind enroute. Follow the link; the wind component parallel to your flight direction will change the range by the product of wind speed times flight time.
Cruise altitude: This depends on the type of engines, jets benefit more from altitude than propeller aircraft.
Temperature

Generally, there should be a chart like this:

It plots the maximum achievable range over the aircraft's payload and assumes that the tanks are filled such that the flight starts with the maximum take-off mass. The chart should also have an explanation that clarifies which altitude and which thrust setting were used.
Or you use approximations like Breguet's range equation, which require detailed knowledge of the aircrafts L/D and the engine's fuel consumption. That will be the weakest point of any range calculation: Sufficient data how changes in the aforementioned parameters affect the result.


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What factors should be included when calculating hourly aircraft operating cost?
I'm working on a budget for operating an aircraft and trying to better understand the hourly operating costs.  What factors should be included that are often forgotten?
Although this is partially discussed here I'm interested in distinguishing between general cost of ownership (hangar, insurance costs, etc.) with items specific to hourly costs. And I'm not looking for actual numbers - just the categories to consider.
Obviously this list will depend upon the type of aircraft, but to keep the question somewhat general, I'm interested in a light single-engined piston aircraft.
So far my categories include:

Cost of fuel per hour
Engine reserve per hour
Prop reserve per hour
Oil cost per hour

Almost no one - at least, no private owner - counts depreciation and cost of capital, but your local flight school almost certainly does (or at least should). But then no one counts them for cars or boats either, that might take the fun out of it :-)

Unless you have a private airstrip and have no intention of insuring the craft you need to include the fixed costs as well. Generally you can do this yearly, then divide by the number of expected hours a year. Some fixed costs are

Storage (hanger or tie down)
Insurance (highly variable)
Annual (this will vary depending on whats broken but there is generally a minimum situation to expect assuming the mechanic finds nothing wrong.
Anything that has less than a 50 hour life time, if you are in this for ownership or renting you are going to fly more than 50 hours a year (I would hope) so you should budget in things like spark plugs, break pads and other high wear parts that get replaced often)

Other reserves may be

Repaint Reserve, this will vary depending on storage and use
Landing Gear Reserve this includes but is not limited to, breaks, tires, shocks, rotors, etc. Budget more if its a complex plane, less if its a Mooney...
Fluid Reserve (not oil) you may also have hydraulic fluid and break fluid.
"Toys" this is money you may chose to add on to your reserve so that you can (down the line) upgrade aging components that may not be broken. For example adding a 430 in place of a radio pair or moving to a full or partial glass cockpit.
Interior, if you are renting this plane and expect it to see heavy use you may want to set some cash aside for the interior. Don't underestimate the difference a warn seat will make vs a fresh seat.

Emergency Fund: This is not a reserve to add to as much as it is cash on hand. If you are renting this plane or even relying on it for heavy personal use you may want to have a budget for emergencies. Especially if you are renting and a down plane means lost rentals. What are you going to do if you need a new fuel tank, or you have a bird strike, or something hits the windshield and cracks it?
Odds and Ends Budget: Nuts and bolts, interior finish screws, that dinky little plastic knob, repainting your yoke, a pitot tube cover (for the 10th time because you lost all the other ones...)

These are all valuable things to consider in the cost of ownership of a plane, however, the OP is specifically looking for things tied to hourly costs. Other than fluids, I believe that everything else you mention really isn't specific to hourly use. (Of course, as a non-pilot, I might be completely wrong...)

Generally these are included but simply divided over the time you fly. Aircraft insurance is often paid upfront unlike car insurance. The landing gear is very much an hourly cost as the parts are swapped on hours like all parts on a plane. Insurance can be related to hours since the more you fly the lower your premiums may be.

I would have thought that gear would be cycle-based, not hour-based, but, I'm not a pilot, so what do I know?!?  That's why I'm here - to learn!

Some parts are but some AD's may require hour based checks like this one for Mooney M20J gear that " Within the next 100 hours time-in-service (TIS) after the effective date of this AD"


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What means do airline ground staff have to converse with pilots in flight?
It seems that airline operational staff on the ground have the ability to initiate verbal communication with airline pilots on at least some airliners, in flight.
Obviously pilots can communicate with ATC using, for example, VHF radio.
Perhaps, even in aircraft where phone service is not available to passengers, pilots in the air and/or airline staff on the ground can

initiate a voice call using telephony equipment that is separate from any PSTN (public switched telephone network)?

using existing headset?
using aircraft internal intercom handsets?
some means of selecting the call recipient?

send text messages over the data links (e.g. via ACARS (Aircraft Communications Addressing and Reporting System) through VHF (very high frequency) or SATCOM (satellite communication))?
use private VHF frequencies to communicate with airline operations?

If any of this is true, how does this work from the perspective of a pilot, steward or an airline operational staff member on the ground?

I've made an edit to generalise and simplify the main question (and remove the subsidiary questions). If you feel the edit is too drastic and would like your original question to get longer exposure in the hope of an answer, please do click the "edited" link and then "rollback". I'd suggest that if you do so, at least move the subsidiary questions into a separate question.

Mobile phones are actually not allowed on aircraft because they wouldn't work well and would exhaust battery rather quickly if left on, so they are not an option. Satellite phones should work though.

@RedGrittyBrick Thanks, looks better now (and I didn't know the right terminology).

Here's at least part of the answer: http://aviation.stackexchange.com/questions/1897/can-airline-pilots-communicate-with-dispatchers

There are numerous methods for air-to-ground communications.  I may be missing a few, but off the top of my head, here are the ones I can remember:

normal VHF comms
Operational staff at the airport maintain an operations frequency that you can use just as you would would ATC.  The limiting factor here is the requirement of line-of-sight with the ground antenna and this limits range.  We could normally raise ops about 30-40 minutes out, at altitude, if someone was actually listening.  This is similar to a GA pilot calling unicom to arrange ground services.  This method is also used for maintenance at some stations and for talking to fuelers and deicing operators.
SELCAL
This is a selective calling protocol that operates over HF and VHF frequencies.  Each participating airplane and ground station (typically a dispatcher or ATC) has a code and if you know the code you want to communicate with, you can establish two-way communications with them.  To use this in the air required tuning a specific frequency and using a hand-mic with a keypad to dial the ground station code.  On the ground I'm not sure the exact method they use (phone patch?) but when they called us we'd get an aural "SELCAL" announced by the airplane along with a light to alert us.
AIRINC phone patch
This service provides VHF-to-PSTN patches and allows you to call your dispatchers actual phone, medlink, or anyone with a phone you feel like calling.  This worked by calling an operator over the normal radios and having them dial a number and connecting us together.
Satellite phone
Works just like any other satellite phone and use the Iridium network.
ACARS
This works just like text messaging.  Select your recipient, type a message and hit send.  You get alerts when messages arrive.  The interface I'm familiar with in the airplane is a program in the FMS with limited pre-set recipients you could contact (dispatch and perhaps a few others).  The ACARS software can also be setup to send specific messages to specific stations, e.g. an "In-Range" message which is routed to operations at your destination.  From the ground side, this is usually baked into the dispatch flight-following software.  Our dispatchers could right click on an airplane, get a menu, pick "text message" and type a message that would be sent to that airplane.

Re satellite phone: So airline staff in the US can use any normal land-line or cell-phone and just dial 011-8816XXXXXXXX. where XXXXXXXXX is a number associated with one of their airline's aircraft?


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When calculating lift, using the the NASA lift equation, can any value be increased, ie. velocity or surface area, for increased lift?
I am trying to understand the breakdown of the NASA lift formula, which is written as such
$L = C_L \frac{\rho v^2}{2}A$
If I take for example CL=0.87, v=20m/s, ρ=1.22kg/m3, and A=9.02m2, my equation looks like this so far: Lift = (1/2) * 0.87 * 1.22 * 20^2 * 9.02. Can any one of those values be increased for greater lift? If I doubled my velocity would I double the lift that the velocity provides? But if I added 25% to the surface area of the wing, my drag also increases. How does that factor into lift? By decreasing velocity?
Does this equation scale in that way? I apologize if it doesn't make sense, I am not sure how to word the question well.

Can any one of those values be increased for greater lift?

Certainly.  But increased lift will not be the only effect.

If I doubled my velocity would I double the lift that the velocity provides? But if I added 25% to the surface area of the wing, my drag also increases. How does that factor into lift? By decreasing velocity?

It doesn't directly factor.  The formula gives you the approximate lift given certain conditions.  It doesn't tell you if those conditions are reasonable or achievable.
You're correct that increasing the wing area or speed will increase drag.  But this equation doesn't tell you how much.  You'd need to look elsewhere to find out the specifics.  The drag increase will not be linear with either one.

Thanks for your reply. I am trying to make sense of building a model of a cargo plane and need to redesign the wing a bit. My best option to increase lift overall would probably be increase wing surface area and velocity, even if drag increases as well? Also, do you know what it is called when things like air and water don't scale?

@Derrick You're looking for the Reynolds number with regard to scaling. If you're interested in designing a model aircraft that will fly, you should get an introductory textbook for aerodynamics. You can change any property of the wing, but it will have other effects besides just increasing lift.

@zaen Thank you! I'll look into it.


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What if a commercial airline pilot misses their flight?
Pilots need to arrive at the airport 1 hour before their departure. What if one of them is not able to report on time (due to any circumstances or reason) and also misses the departure time of flight.

In that situation, will the flight get delayed?
Will the airline wait for the pilot to come or will they find some other pilot for this flight?
Are there any extra pilots always available for handling this kind of situation?
What action will be taken against the pilot for missing the flight?
Can this type of issue have any effect on a pilot's career (like any kind of ban or suspension or penalty)?

I would split this question into two: one about the operation, the other about the career.

Technically I think it is impossible for a pilot to miss his flight ...

@J.Hougaard -- clever, although one can certainly be late for one's flight, causing it to be similarly tardy.  And missing "the flight that was yours, right up until it wasn't yours any longer because you weren't going to be there for it" is more cumbersome than talking about missing "your" flight.

On hold for too broad, yet easily answered below...

Spot on @Michael Hall

@MichaelHall indeed. A comprehensive answer, dealing with all the connected issues, consequences and solutions to pilots missing their schedule. The subject belongs in one place, rather than in a series of partial questions.

I agree.  I just wish we didn't have certain individuals shutting the door on competing answers over personal opinion about the question. Yes, there are some bad questions, and it is appropriate to close some, but often keeping a multi-part Q and A in the same location will provide a deeper understanding than if you were to break this into 5 separate parts. What do you say bogl, xxavier, Bianfable, J. Hougaard, and kevin? Why not allow others to answer and let the voters decide?!

@MichaelHall, I see 6 questions and proposed to split in 2, because I really see two different topics. The point is not if the questions can be answered, but how to deal with different answers that cover only some of the questions.

Also see the FAQ and related QA on meta: https://meta.stackexchange.com/questions/120633/what-do-we-do-with-multiple-question-questions

@bogl - You certainly have a right to your opinion, I just don't think you should shut down others on that basis.

@MichaelHall  Sorry, I didn't shut anybody down. I am not a moderator, and I don't have such privileges. I gave my vote in a regular review process, and in addition I made a constructive suggestion. If you have concerns, questions or doubts about this process, you should really start a discussion on https://aviation.meta.stackexchange.com/

"Put on hold as too broad by bogl…"  Scroll up and see for yourself.

@MichaelHall You might want to have a look at https://meta.stackexchange.com/questions/161390/what-are-the-review-queues-and-how-do-they-work

OK, I admittedly scanned through it quickly, but I do not see anything in the link refuting my observation that you put this question on hold, thereby squelching any subsequent answers.  Got a quote or section you can refer me to?

@MichaelHall I am tired of this. The documentation is in front of you. If it is unclear, by all means, please ask a question on Meta!

Me to.  I provided a specific quote to back my position and you provided nothing to refute it.

@MichaelHall please come to chat. And please be aware that unless a ♦ mod is involved, 5 users are needed to put a question on hold. And that a question on hold is not "shut down", is on hold to be improved before people invest time to answer it.

An antidotal answer as don’t have an official source but until Flybe recently went out of business, their method was to have a backup crew on call for each airport. If you were on call you had to be able to get to the airport within 60 minutes to cover someone phoning in sick. I believe other airlines run similar setups.

Sometimes one of the passengers flies the plane if a pilot is missing (happened a few days ago in Manchester).

Airlines try to maintain some ratio of crews to fleet to provide surplus bodies to cope with this sort of thing.  For Regionals, where the average aircraft hours are around 2500 hrs per year, and each pilot flies somewhere around 800-1000 hrs per year, you need 3 crews per a/c just to meet the baseline operational need.  Add absentee time for vacation requirements and booking off sick, training etc, and you need 4-5 crews per a/c to be able to sure that you can keep each airplane running 2500 hrs/year.
As a result, Regional operators will try to keep about 8-10 pilots on staff per aircraft and if they are below that, problems start to happen.  You can get by somewhat with crews working overtime, but there are limits to that due to regulatory duty limits.  Airlines have a reserve system to organize crews to make sure there are available idle bodies to step in if required.
There is "reserve" and "ready reserve" duty.  Reserve duty is being on-call at or near home and able to report within a reasonable time of being called, like 2 hours.  These are to cover book-offs with advance notice, like a pilot calling in sick 6 hours before.  Ready reserve duty is where the pilot has to go to the airport crew ops office in uniform and basically hang around ready to go on short notice for someone who doesn't show or who calls in at the last minute.
So:

Yes probably, if there isn't a ready reserve pilot on hand.
They'll stick in a guy/gal on ready reserve if they have one.  If not, the flight will get delayed or cancelled.
See above.
Booking off sick or calling in because you had a traffic accident or home crisis isn't a problem.  The problem is failing to call in and leaving people hanging.  You better have a very good reason for not showing up and not calling in.  That would result in some kind of disciplinary ding on your record, getting worse if you do it more than once.  It would depend on an airline's union contract, or if non-union, the management's disciplinary policy.
In a union shop, for a one time thing, probably not if not repeated.  Union shops give you the luxury of having to screw something up several times to really get hammered for things that are not safety related. It'll depend on contract language; but you could get suspended or let go eventually.  In a non-union shop, it could hurt you in terms of promotion, or if you did it more than once you might get let go more readily than at a unionized airline.

Bottom line is, the next worst thing to unsafe pilots are unreliable pilots.
In the Regional airline business especially, the shortage of crews is really starting to bite and airlines are not able to maintain the necessary staffing "fat" as the flow from the bottom thins out and the majors suck up the experienced crews.  Many cancelled flights with Regional operators are due to lack of crews, not mechanical or weather issues.  The 1500 hr "Colgan Rule" requirement in the US has made this that much more severe, but up here in Canada where Regionals can still take 250 hour flight school graduates under special programs where they are groomed in-house, there are still not enough to cope with retirements and flights are being cancelled for lack of crews.
This is all tied to the final stages of the movement of the "baby boom" demographic wave, which is now resulting in a flood of retirements of airline capts born in the mid 50s hitting retirement age, which should finally start to taper off in the next 10 years once the peak of the wave is mowing the lawn at home.  Everybody's vacuuming up pilots from the levels below them, resulting in shortages all the way down the chain.

Worth noting that some of the above also applies to Flight Attendants because dependent on the aircraft a certain number of them is required as well, see here for the regulations.

Yes good point.  FA's are basically riot cops, trained in the control of crowds and chaos, almost all of whom spend their entire careers working undercover so to speak as stewards and servers.


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What is the correct equation for rotor solidity?
I'm working in a project that uses"blade solidity ratio", or "rotor solidity", the problem is, there are several articles which defines the equation in a different way changing in the section of the Radius analysis. I found 3 equations that I will describe below:
$$1. \frac{Nc}{2πR}$$ $$2. \frac{Nc}{2R}$$ $$3. \frac{Nc}{R}$$
N=Number of Blades, c= Chord Length, R= Radius of the rotor
Which one is correct or there is some case where each of this equation is applied?
Thanks.

Rotor solidity is the area of the rotor disk that is actually occupied by blade area.
Area of rotor blades = $N \cdot c \cdot R$
Area of rotor disk = $\pi \cdot R^2$
$$Rotor \ solidity = \frac{N \cdot c}{\pi \cdot R} \tag{4}$$
So all three of the equations OP found would not be usual. Good reference books are:

Helicopter Performance, Stability and Control by Raymond R. Prouty
Principles Of Helicopter Aerodynamics by J. Gordon Leishman.

Both these books use equation (4) for rotor solidity. It is possible for a factor 2 to pop up in the coefficients which are usually considered regarding disk area and solidity: $C_T, C_P$ and $C_Q$. From Leishman:

This is generally correct, but if a paper defines it differently and then presents results with respect to it, then that definition should be used for those results/formulae. I've also seen different definitions of solidity (usually for aeroplane propellers though), presumably to account for typical blade shapes etc.

Thanks for your response, this was very helpful.

Actually, you've got to be a little careful about your nomenclature here because its easy to compare x2 (unfortunately similarly) named concepts here (which is very common even among people in the industry). That is, although "blade" and "rotor" solidity are very similarly named, they are in fact different - that is why you find two different definitions (one based on chord vs pitch (blade solidity) and one based on areas (blade area vs disc area)), irrespective of the fact that you have also (as other commentators have pointed out, found a variation, but dimensionally consistent definitions for the latter).

Blade solidity - conventionally $\frac{c}{s}$, is the ratio of (true) chord to pitch. In British literature, the inverse concept of pitch-to-chord ratio ie $\frac{s}{c}$ is much more commonly used.
Essentially, this is useful when trying to estimate the number of blades, since conceptually, you can imagine, the longer the chord of a lifting surface, the more ability it has to effect "turning" in the general freestream flow. So conversely, if you want to aerodynamically deflect ("turn") a lot of air, you either need one large aerofoil or lots of little ones (shorter chord) stacked closely together. Since blade solidity is mostly a concept used in turbomachinery, its easiest to imagine how blades on a hub would affect the axial flow. Either I used a few large "fat" blades, and impart a lot of turning in the flow, or I can use a lot of smaller blades to result in the same effect. The same effect can be visualised in the downwash of a wing - a large, deep chord A380 main wing is going to induce a lot of downwash into all the freestream (even that far from the wing) simply because its so large, or I can use a lot of smaller individual "wings" to get the same effect.

Rotor solidity - generally $\frac{A_{blades}}{A_{disc}}$ $(= \frac{Nc}{\pi R})$ (for rectangular blades), is a measure the closeness of the actual rotor area to that of the well known theoretical "actuator disc" concept, used in momentum theory.
Basically its used as a similarity parameter to allow for comparison of the characteristics of different rotor planforms, for example, how a rotor with long, high aspect ratio blades compares to a rotor with the same solidity but comprised of perhaps more blades but lower aspect ratios.

Undoubtedly you could make some tenuous links between the two, if you made assumptions about things like blade shapes, but because fundamentally, the definitions are different, they're similar but different concepts. For example, while its completely possible for blade solidity to be greater than 1 (for example for a turbine stator blade to have a chord longer than its pitch), rotor solidity is always less than 1, and generally much lower than the former.
Practically, conventional gas turbine turbomachinists are going to be much more interested in blade solidity, since naturally the pitch between adjacent blades is going to change with radius, which might then affect your selection of aerofoil chord length at that given radial station, whereas aero guys looking at helicopter blades, wind turbines and things like propellers etc are going to use rotor solidity more to compare efficiencies of different planform designs but with the same rotor solidity.

Dimensionally, those expressions are the same (and thus comparable), except of course for the $2\pi$ constant.
Check the rest of the equations, it is very likely the numeric factor is simply elsewhere.

I would say that each article with expressions should be analyzed separately, because if the cross-flow turbine is viewed from the upwind side then it covers for wind a rectangular area corresponding to pseudo solidity at expression 2, but considering that at crossflow turbines down the wind side of this area are the same blades obstructed the same rectangular area, then the solidity meets 2 times higher, which corresponds to expression 3.


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What flight controls should be used to counter asymmetric yaw?
How should the autopilot or pilot handle asymmetric yaw, as with one failed engine on a multi-engine turboprop whose engines are not on the centerline?
Should one apply roll control or rudder control?

The details will depend on the exact aircraft type, so I will answer for the Bombardier Dash-8 Q400 as an example.
The autopilot does not have rudder authority on the Dash-8 (source: FCOM Autoflight chapter):

12.3.7 Autopilot
The Autopilot (AP) couples the FD commands to the flight control surfaces using pitch and roll servos for automatic control of the aircraft flight path.

If not disengaged, the autopilot would try to maintain heading with roll only.
The yaw damper would not be enough to overcome the yaw asymmetry either:

12.3.9 Yaw Damper
The Yaw Damper provides through control of the rudder:

Damping of the aircraft Dutch Roll mode.
Turn coordination.

The Yaw Damper authority is limited to a maximum of ± 4.5 degrees of rudder by mechanical stops. Yaw Damper commands are limited in software as a function of airspeed.

The correct procedure in case of an engine failure would be to hold rudder towards the live engine and then trim the rudder whenever time permits:

(image source: FCOM Flight Controls chapter)

RUDDER TRIM INDICATOR

indicates trimmed rudder position

RUDDER TRIM KNOB (rotary action spring loaded to neutral)
  ROTATE

trims rudder in desired direction
first graduation trims slow, second graduation trims fast

The target for the rudder trim should be coordinated flight, i.e. no sideslip indicated on the primary flight display (PFD):

(image source: FCOM Indicating and Recording Systems chapter)

SLIP/SKID INDICATOR (white)

the Slip/Skid Indicator shows the lateral acceleration of the aeroplane and is a trapezoid symbol. It turns with the roll pointer
the maximum deflection indication shows a 0.14 g lateral acceleration. This is equivalent to one and a half the thickness of the upper part of the slip/skid symbol (trapezoid shape)
the slip skid Indicator is shown to the left when the aeroplane is slipping to the right and to the right when the aeroplane is slipping to the left
the indicator goes out of view when the aeroplane roll is more than 60 degrees or the related AHRU attitude has malfunctioned

Excellent answer. I will just add that in an engine out scenario you actually want a small angle of bank with ball displaced about a half ball out for the best performance.  There is a good article explaining why here:  http://www.cast-safety.org/pdf/5_asymmetric_flight.pdf


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What happens to jettisoned fuel tanks?
When an F-15 (or your favorite fighter aircraft) punches it's external tanks...

...to engage in combat, (or when they are empty), what happens to them?
Through my best reasoning skills and Newton's calculations, I have determined that they will fall.
But what happens when they hit the ground? Do they explode? Do they detonate at a certain height? Is this a problem? Are there regulations determining where/when pilots may pickle their tanks? Have there ever been any accidents? (E.g. houses/cows/grandmothers destroyed by falling fuel tanks?)

They are called drop tanks. When a drop tank is jettisoned, very likely it is not retrieved and reused. This is also the case with (sadly, discontinued) Space Shuttle external tank. Those tanks were not reused either. I am not talking about the rocket boosters.
What happens to jettisoned fuel tanks?
It depends on where they land. The tanks jettisoned in Vietnam have been used to make boats (more pictures here).
It is worth noting that these external fuel tanks have disadvantage too:

A general rule is that only about half the capacity of a streamlined
  drop tank actually goes towards increasing the aircraft's overall
  range, the rest going to overcome the added drag and weight of the
  tank itself.

It's more likely that they don't ditch tanks just because they are empty, they are reusable and not cheap and may still have some dregs of fuel in them. Besides ecologists already hate the military no need to aggravate them further.
A tank dropped for another reason drop and drill itself into the ground and may or may not survive in one piece. An explosion is unlikely unless there is an ignition source to spark the explosion.

Surely a metal tank hitting an asphalt road (read: sparks) is enough to ignite?

@HCBPshenanigans you'd be amazed how hard a nearly empty fuel tank is to ignite, don't believe hollywood's one-scratch-and-boom engineering examples.

I would say a nearly empty fuel tank is much easier to ignite than a full one, since the vapor is what ignites, not the fuel(liquid).

@HCBPshenanigans It's still pretty tough to get a fuel tank to ignite, even when you're trying. You need a good hot spark (in a confined area), or other source of ignition - hot pavement probably won't do the job.

Hmm, it seems you are right about the price. I would've assumed they were cheap 'throwaway' price. "A drop tank is quite pricy (think high end BMW prices). They are every bit as complex as the wing they attach to. Most have multiple cells to maintain CG and all the plumbing, pumps, valves, pressurization, feed and gaging as the remainder of the fuel system. Then add aerodynamic considerations, explosives for safe separation and maybe some RAM for low observables."

@HCBPshenanigans they get crushed, even if they rupture as a result any vapours will spread too fast for a combustible mixture to exist. As to price, depends heavily on the tank. And of course as a fraction of the cost of running a mission, the cost of a drop tank is often not that much...

@HCBPshenanigans Take some AVTUR.  Pour it onto the road on a cold day.  Throw a lit match into it.  The match will go out.  (Hint, don't try this with AVPIN ;)